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A quadratic form Q(z) is said to be positive definite if Q(z)>0 for z!=0. A real quadratic form in n variables is positive definite iff its canonical form is ...

The resolution principle, due to Robinson (1965), is a method of theorem proving that proceeds by constructing refutation proofs, i.e., proofs by contradiction. This method ...

An ansatz is an assumed form for a mathematical statement that is not based on any underlying theory or principle. An example from physics is the Bethe Ansatz (Müller).

When the Gaussian curvature K is everywhere negative, a surface is called anticlastic and is saddle-shaped. A surface on which K is everywhere positive is called synclastic. ...

A homographic transformation x_1 = (ax+by+c)/(a^('')x+b^('')y+c^('')) (1) y_1 = (a^'x+b^'y+c^')/(a^('')x+b^('')y+c^('')) (2) with t_1 substituted for t according to ...

For positive numbers a and b with a!=b, (a+b)/2>(b-a)/(lnb-lna)>sqrt(ab).

An asymptotic direction at a point p of a regular surface M in R^3 is a direction in which the normal curvature of M vanishes. 1. There are no asymptotic directions at an ...

Given a function f(x) plotted in the Cartesian plane as y=f(x), the average rate of change (or average rate of change function) of f from x to a is given by ...

A method for mapping three-dimensional figures onto the plane.

The azimuthal angle is an angle measured from the x-axis in the xy-plane in spherical coordinates, denoted theta in this work.